$$ \begin{aligned} -\frac{1}{3} &= \frac{1}{2}x+\frac{2}{7}&& \text{multiply ALL terms by } \color{blue}{ 42 }. \\[1 em]-42\cdot\frac{1}{3} &= 42 \cdot \frac{1}{2}x+42\cdot\frac{2}{7}&& \text{cancel out the denominators} \\[1 em]-14 &= 21x+12&& \text{ swap the left and right side of the equation } \\[1 em]21x+12 &= -14&& \text{ move 12 to the right } \\[1 em]21x &= -14-12&& \\[1 em]21x &= -26&& \text{ divide both sides by $ 21 $ } \\[1 em]x &= -\frac{26}{21}&& \\[1 em] \end{aligned} $$

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